Abstract
The traditional method of fundamental solution (T-MFS) is known as an effective method for solving the scattering of elastic waves, but the T-MFS is inefficient in solving large-scale or broadband frequency problems. Therefore, in order to improve the performance in efficiency and memory requirement for treating practical complex 2-D broadband scattering problems, a new algorithm of fast multi-pole accelerated method of fundamental solution (FM-MFS) is proposed. Taking the 2-D scattering of SH waves around irregular scatterers in an elastic half-space as an example, the implementation steps are presented in detail. Based on the accuracy and efficiency verification, the FM-MFS is applied to solve the broadband frequency scattering of plane SH waves around group cavities, inclusions, a V-shaped canyon and a semi-elliptical hill. It shows that, compared with T-MFS, the FM-MFS has great advantages in reducing the consumed CPU time and memory for 2-D broadband scattering. Besides, the FM-MFS has excellent adaptability both for broad-frequency and complex-shaped scattering problems.
Highlights
The scattering of elastic waves is an attractive and significant topic in many fields such as in earthquake engineering, geophysics, civil engineering, etc
The numerical methods include finite difference methods (FDM) [9, 10], finite element methods (FEM) [11, 12], boundary element methods (BEM) [13,14,15,16,17,18,19,20], and more works can be found in a review by Sanchez-Sesma et al [21] and by Manolis and Dineva [22]
The method of fundamental solution (MFS) can be regarded as a special indirect boundary integral equation method which is very similar to the Trefftz method [23]
Summary
The scattering of elastic waves is an attractive and significant topic in many fields such as in earthquake engineering, geophysics, civil engineering, etc. A FAST-MULTI-POLE ACCELERATED METHOD OF FUNDAMENTAL SOLUTIONS FOR 2-D BROADBAND SCATTERING OF SH WAVES IN AN INFINITE HALF SPACE. A significant weakness of MFS is that the calculation efficiency of solving high-DOF problem (such as large scale, broadband frequency or multi-body scattering) is seriously affected by its dense characteristic of the equation matrix. In order to overcome the disadvantage of traditional MFS and solve large-scale elastic wave-motion problems in a half-space, a new algorithm of the FM-MFS is proposed and validated. The scattering of plane SH waves by randomly distributed cavity or inclusion group, by a canyon and hill topography in a half-space are solved and discussed
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